Cubic Bezier approximation of a digitized curve

摘要

In this paper we present an efficient technique for piecewise cubic Bezier approximation of digitized curve. An adaptive breakpoint detection method divides a digital curve into a number of segments and each segment is approximated by a cubic Bezier curve so that the approximation error is minimized. Initial approximated Bezier control points for each of the segments are obtained by interpolation technique i.e. by the reverse recursion of De Castaljau's algorithm. Two methods, two-dimensional logarithmic search algorithm (TDLSA) and an evolutionary search algorithm (ESA), are introduced to find the best-fit Bezier control points from the approximate interpolated control points. ESA based refinement is proved to be better experimentally. Experimental results show that Bezier approximation of a digitized curve is much more accurate and uses less number of points compared to other approximation techniques. (c) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.